Fundamental Solutions for In-Plane and Out-of-Plane Problems of Viscoelastic Medium with Circular or Elliptic Hole and Their Numerical Examples

Abstract

Time dependent behavior of viscoelastic medium with an circular or elliptic tunnel is investigated by use of the correspondence principle between elasticity and viscoelasticity. The closed-formed analytical solutions for stress and displacement are obtained for the cases of in-plane and out-of-plane problems under concentrated forces and dislocations. The viscoelastic behavior of the medium is adopted to be represented by typical rheology models such as Burgers or Standard model for deviatoric stress and Elastic model for volumetric stress. Several numerical examples are shown by graphical representations.